I would look into an anti-inflammatory diet. There is a discussion thread here on WTM, but I would recommend reading one of the books,
Inflammation Nation by Floyd Chilton, Ph.D. to give you a good working knowledge of the dietary guidelines. There are LOTS of "anti-inflammation" diets listed on the internet and recommended by various practitioners, and there are conflicting lists of foods. Chilton's book is based on clinical findings and will explain HOW various foods affect the immune response, so that you are able to choose better options for you/your family. I much prefer his reasoning and analysis.
Asthma is common in my family. I was diagnosed as a child. However, I haven't suffered from it since I changed my diet. I eat differently than the rest of my family. They all say it takes too much time and/or money to change, so they continue to use their medications. Also, their doctors tell them that asthma has no 'cure.' Maybe not, but I haven't had an episode in over 30 years.
Over the years, I have eliminated canned and processed foods (including white sugar). Luncheon meats, cured meats, smoked meats, meats with nitrates and meats with nitrites have been eliminated. Boxed foods, bagged foods, and frozen, pre-packaged heat and serve meals are gone. Over time, I have further refined this to include organic produce and some organic meats. For a long time, I did not consume dairy products. Now, I consume non-homogenized, unpasteurized milk (raw, whole) products. I do not drink milk as a beverage, but I do use it's fermented products like yogurt, cheese, kefir and whey as ingredients in my cooking. For me, I have found that this moderate use of raw milk and raw milk products does not create the same response as the normal grocery store product (pasteurized, homogenized, vitamin A & D added, etc.)
That sounds all too limiting until you look at what I DO consume. I've had to learn how to cook from scratch and/or find sources of good quality pre-prepared foods. We enjoy a variety of vegetables (lots of greens) and meats. Our foods are sweetened with stevia, agave nectar, black cherry concentrate, dates and whatever other whole food sweetener I find. Our sandwiches are made with organic mayonnaise on whole grain sprouted bread. We have kosher hot dogs, organic chicken salad, etc. Salmon, cod, whiting and other ocean caught wild fish are eaten regularly. We enjoy ground beef, steak, roast, LOTS of organic chicken. I could go on, but you get the idea. These guidelines are limiting, but there is a ton of variety within them. AND over time, you will find ways to make the dollars stretch as you find ways to make your own dishes with the added bonus that you don't have to spend $ on medications to suppress your immune response.
I don't mean to sound like I think the 'food police' should come and clean out your pantry. I don't. I just don't like to see people suffering with all sorts of medical interventions when their symptoms could be alleviated by something as simple as a few dietary changes. I've seen too many children on oxygen in the hospital with breathing therapies because their family is convinced that they just cannot afford to live without processed foods.

I'm not saying dietary changes would correct every case, but I do honestly believe that dietary changes would improve all cases and at least reduce the frequency of needed medical intervention.
Just my $.02